"Twice more than (two times more)" vs "Twice as much"

A common mistake by my student is "twice more than", they often mistake it as "twice as much as". Actually they are different:

•   Twice as much = 2 X the base
•      Twice more than (Two times more) = 2 X the base + the base

Here is an example:

Tom's present age is twice more than Sam's age years ago. Today, Sam's age is Tom's age the same number of years ago. How old is Tom now if the sum of their present age is 30?

Solution:

In this question, "Tom's present age is twice more than Sam's age years ago", means Tom's present age is 3u, Sam's age years ago is 1u.

'Buy two get one free' Question

Question:

Mr Lee bought some files at $4 each and sold them at $10 each. The customers who bought 2 files from him were given 1 file for free. Yesterday, all his customers bought either one or two files. At the end of the day, he had given away 120 files and had earned $1230. Find the number of customers who bought only one file. 

Solution:

'Set' Question

Question: 



Solution:

It can be solved using 'set'

1 set --> 8 bags of sweets and 1 bag of chocolate
Money collected for 1 set --> 8 x 5.5 + 2 = 46
No. of sets = 3128 / 46 = 68

No. of sweets sold --> 68 x 8 x 4 = 2176
No. of chocolates sold --> 68 x 8 = 544

Another Model Question

Question: 

Alex, Ben and Caleb had some stamps. Alex had 90 stamps more than Ben, and Ben had 10 stamps more than Caleb. After Alex had given Ben 95 of his stamps and Caleb bought some stamps, Alex and Caleb had the same number of stamps while Ben had thrice as much as either of them.

a) How many stamps did Caleb have at first?
b) How many stamps did they have altogether at first?

Solution:

Two Math Questions

Two questions from Belnanna:

Question 1:

In a school science fair, there were exhibits from class A , class B and class C. Altogether, 25 exhibits came from class B and class C. In a total of 16 exhibits were not from class C and a total of 15 exhibits were not from class B.
How many exhibits were there altogether?

Solution:

16 exhibits not from C --> A + B = 16
15 exhibits not from B --> A + C = 15
2A + B + C = 31
B + C = 25
2A --> 6
A --> 3
B --> 13
C --> 12
Total exhibits --> 3 + 13 + 12 = 28


Question 2:

The length of a rectangular pond is 14 m and its breadth is 7 m. Fatimah wants to build a running path around the pond. The width of the path is 1/2 m. what is the area of the running path?

Solution:

LCM Method

A question from Kiasuparents:

A group of people met at a party. Each person shook hands with everyone else. Mr Ong shook hands with 4 times as many men as women and Mrs Ong shook hands with 5 times as many men as women. How many women were there at the party ?

Solution: